This document provides an overview and examples of using the graph-and-check method to solve systems of linear equations in two variables. It introduces linear systems and explains that the solution is an ordered pair that satisfies both equations. Two examples are worked through step-by-step showing how to graph the lines and check that the point of intersection satisfies the equations. Students are assigned practice problems applying this method.

1. Chapter 7
Systems of Equations &
Inequalities
P. 424
Prerequisite Skills

2. • In this chapter, you will learn three
different methods to solve a pair of linear
equations simultaneously.
• We will also learn the difference between
solving an equation and solving an
inequality.

3. • Section 7.1 Solve Linear Systems by
Graphing (Graph & Check Method)
•
P. 427
This is the first of three method to solve a
linear system.

4. Linear System:
A system of linear equations (or simply a
linear system) consists of two or more
linear equations in the same variables.
Example: x + 2y = 7
3x – 2y = 5

5. The solution of a system of linear equations
in two variables is an ordered pair that
satisfies each equation in the system.

6. EXAMPLE 1 Check the intersection point
Use the graph to solve the
system. Then check your
solution algebraically.
x + 2y = 7 Equation 1
3x – 2y = 5 Equation 2
SOLUTION
The lines appear to intersect at the point (3, 2).
CHECK Substitute 3 for x and 2 for y in each equation.
x + 2y = 7
?
3 + 2(2) = 7
7=7

7. EXAMPLE 1 Check the intersection point
3x – 2y = 5
?
3(3) – 2(2) = 5
5=5
ANSWER
Because the ordered pair (3, 2) is a solution of each
equation, it is a solution of the system.

8. EXAMPLE 2 Use the graph-and-check method
Solve the linear system:
–x + y = –7 Equation 1
x + 4y = –8 Equation 2
SOLUTION
STEP 1
Graph both equations.

9. EXAMPLE 2 Use the graph-and-check method
STEP 2
Estimate the point of intersection. The two lines
appear to intersect at (4, – 3).
STEP 3
Check whether (4, –3) is a solution by substituting 4 for
x and –3 for y in each of the original equations.
Equation 1 Equation 2
–x + y = –7 x + 4y = –8
? ?
–(4) + (–3) = –7 4 + 4(–3) = –8
–7 = –7 –8 = –8

10. EXAMPLE 2 Use the graph-and-check method
ANSWER
Because (4, –3) is a solution of each equation, it is a
solution of the linear system.

11. GUIDED PRACTICE graph-and-checkand 2
EXAMPLE 2 Use the for Examples 1 method
Solve the linear system by graphing. Check your solution.
3. x – y = 5
3x + y = 3
ANSWER
(2, 3)

12. • Assignment: P. 430- 431
Do # 1-5 orally together
• Write out / graph 8-10, 12-14, 18-20
• Remember to CHECK your solution in
both equations.